Magnetic relaxation and correlating effective magnetic moment with particle size distribution in maghemite nanoparticles

Abstract

The role of particle size distribution inherently present in magnetic nanoparticles (NPs) is examined in considerable detail in relation to the measured magnetic properties of oleic acid-coated maghemite (γ-Fe2O3) NPs. Transmission electron microscopy (TEM) of the sol–gel synthesized γ-Fe2O3 NPs showed a log-normal distribution of sizes with average diameter 〈D〉=7.04nm and standard deviation σ=0.78nm. Magnetization, M, vs. temperature (2–350K) of the NPs was measured in an applied magnetic field H up to 90kOe along with the temperature dependence of the ac susceptibilities, χ′ and χ″, at various frequencies, fm, from 10Hz to 10kHz. From the shift of the blocking temperature from TB=35K at 10Hz to TB=48K at 10kHz, the absence of any significant interparticle interaction is inferred and the relaxation frequency fo=2.6×1010Hz and anisotropy constant Ka=5.48×105erg/cm3 are determined. For T<TB, the coercivity HC is practically negligible. For T>TB, the data of M vs. H up to 90kOe at several temperatures are analyzed two different ways: (i) in terms of the modified Langevin function yielding an average magnetic moment per particle μp=7300(500) μB; and (ii) in terms of log-normal distribution of moments yielding 〈μ〉=6670µB at 150K decreasing to 〈μ〉=6100µB at 300K with standard deviations σ≃〈μ〉/2. It is argued that the above two approaches yield consistent and physically meaningful results as long as the width parameter, s, of the log-normal distribution is less than 0.83.